\documentclass[9pt]{article}
\usepackage{amsmath}
\begin{document}
Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  21.0 & -1.00 x_{1} & -2.00 x_{2} & -10.00 x_{3} & +  3.00 x_{4} & + 10.00 x_{5} & -10.00 x_{6} & -2.00 x_{7} & +  5.00 x_{8} & +  3.00 x_{9}\\
 x_{11}   &  -53.0 & + 10.00 x_{1} & + 10.00 x_{2} & -8.00 x_{3} & +  9.00 x_{4} & + 10.00 x_{5} & +  4.00 x_{6} & +  5.00 x_{7} & +  5.00 x_{8} & +  4.00 x_{9}\\
 x_{12}   &  11.0 & -7.00 x_{1} &   & -7.00 x_{3} & +  9.00 x_{4} & -10.00 x_{5} &   & +  4.00 x_{7} & -3.00 x_{8} & -6.00 x_{9}\\
 x_{13}   &  26.0 & +  7.00 x_{1} & -4.00 x_{2} & +  4.00 x_{3} & +  1.00 x_{4} & -4.00 x_{5} & -4.00 x_{6} & -3.00 x_{7} & + 10.00 x_{8} & +  1.00 x_{9}\\
 x_{14}   &  -35.0 & +  7.00 x_{1} & -10.00 x_{2} & -6.00 x_{3} & +  6.00 x_{4} & +  7.00 x_{5} & + 10.00 x_{6} & +  1.00 x_{7} & -2.00 x_{8} & +  3.00 x_{9}\\
 x_{15}   &  -14.0 & +  5.00 x_{1} & -4.00 x_{2} & +  2.00 x_{3} & + 10.00 x_{4} & -3.00 x_{5} & -1.00 x_{6} & -1.00 x_{7} & -5.00 x_{8} & -6.00 x_{9}\\
 x_{16}   &  -27.0 & -2.00 x_{1} & + 10.00 x_{2} & +  2.00 x_{3} & +  5.00 x_{4} & +  9.00 x_{5} & +  3.00 x_{6} & -8.00 x_{7} & +  6.00 x_{8} & -1.00 x_{9}\\
 x_{17}   &  52.0 & +  4.00 x_{1} & -8.00 x_{2} & +  5.00 x_{3} & -7.00 x_{4} & -10.00 x_{5} &    &   & -2.00 x_{8} &   \\
 x_{18}   &  -44.0 & +  6.00 x_{1} & -9.00 x_{2} &   & +  1.00 x_{4} & + 10.00 x_{5} & +  1.00 x_{6} & +  9.00 x_{7} & +  8.00 x_{8} &   \\
\hline
z    &  0.0 & +  5.00 x_{1} & -1.00 x_{2} & +  3.00 x_{3} & +  5.00 x_{4} & +  1.00 x_{5} & +  3.00 x_{6} & +  1.00 x_{7} & -2.00 x_{8} & -2.00 x_{9}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{9}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,18$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & +  1.00 y_{10} & -10.00 y_{11} & +  7.00 y_{12} & -7.00 y_{13} & -7.00 y_{14} & -5.00 y_{15} & +  2.00 y_{16} & -4.00 y_{17} & -6.00 y_{18}\\
 y_{2}   &  1.0 & +  2.00 y_{10} & -10.00 y_{11} &   & +  4.00 y_{13} & + 10.00 y_{14} & +  4.00 y_{15} & -10.00 y_{16} & +  8.00 y_{17} & +  9.00 y_{18}\\
 y_{3}   &  1.0 & + 10.00 y_{10} & +  8.00 y_{11} & +  7.00 y_{12} & -4.00 y_{13} & +  6.00 y_{14} & -2.00 y_{15} & -2.00 y_{16} & -5.00 y_{17} &   \\
 y_{4}   &  1.0 & -3.00 y_{10} & -9.00 y_{11} & -9.00 y_{12} & -1.00 y_{13} & -6.00 y_{14} & -10.00 y_{15} & -5.00 y_{16} & +  7.00 y_{17} & -1.00 y_{18}\\
 y_{5}   &  1.0 & -10.00 y_{10} & -10.00 y_{11} & + 10.00 y_{12} & +  4.00 y_{13} & -7.00 y_{14} & +  3.00 y_{15} & -9.00 y_{16} & + 10.00 y_{17} & -10.00 y_{18}\\
 y_{6}   &  1.0 & + 10.00 y_{10} & -4.00 y_{11} &   & +  4.00 y_{13} & -10.00 y_{14} & +  1.00 y_{15} & -3.00 y_{16} &   & -1.00 y_{18}\\
 y_{7}   &  1.0 & +  2.00 y_{10} & -5.00 y_{11} & -4.00 y_{12} & +  3.00 y_{13} & -1.00 y_{14} & +  1.00 y_{15} & +  8.00 y_{16} &   & -9.00 y_{18}\\
 y_{8}   &  1.0 & -5.00 y_{10} & -5.00 y_{11} & +  3.00 y_{12} & -10.00 y_{13} & +  2.00 y_{14} & +  5.00 y_{15} & -6.00 y_{16} & +  2.00 y_{17} & -8.00 y_{18}\\
 y_{9}   &  1.0 & -3.00 y_{10} & -4.00 y_{11} & +  6.00 y_{12} & -1.00 y_{13} & -3.00 y_{14} & +  6.00 y_{15} & +  1.00 y_{16} &    &   \\
\hline
z    &  -0 & -21.00 y_{10} & + 53.00 y_{11} & -11.00 y_{12} & -26.00 y_{13} & + 35.00 y_{14} & + 14.00 y_{15} & + 27.00 y_{16} & -52.00 y_{17} & + 44.00 y_{18}\\
\end{array}\]
Initialization succeeded in finding final dual dictionary with 11 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{16}   &  0.0106208168009 & -0.75 y_{10} & +  0.03 y_{7} & -0.23 y_{14} & +  0.41 y_{13} & -0.04 y_{4} & +  0.05 y_{1} & -0.05 y_{5} & +  0.97 y_{17} & -0.23 y_{11}\\
 y_{12}   &  0.0114223878802 & -0.10 y_{10} & -0.04 y_{7} & +  0.21 y_{14} & +  0.57 y_{13} & -0.04 y_{4} & +  0.07 y_{1} & -0.00 y_{5} & +  0.55 y_{17} & +  0.13 y_{11}\\
 y_{3}   &  0.914592601499 & + 10.36 y_{10} & -0.41 y_{7} & +  9.17 y_{14} & +  0.89 y_{13} & -0.11 y_{4} & +  0.56 y_{1} & +  0.04 y_{5} & -2.41 y_{17} & + 11.02 y_{11}\\
 y_{18}   &  0.123482024769 & -0.37 y_{10} & -0.06 y_{7} & -0.48 y_{14} & +  0.35 y_{13} & -0.02 y_{4} & +  0.00 y_{1} & -0.04 y_{5} & +  0.58 y_{17} & -0.91 y_{11}\\
 y_{2}   &  2.29337501503 & +  6.92 y_{10} & -0.76 y_{7} & +  5.48 y_{14} & -0.37 y_{13} & +  0.00 y_{4} & -0.80 y_{1} & +  0.26 y_{5} & +  2.18 y_{17} & -19.16 y_{11}\\
 y_{6}   &  0.916716764859 & + 12.81 y_{10} & -0.00 y_{7} & -9.47 y_{14} & +  1.57 y_{13} & +  0.08 y_{4} & -0.23 y_{1} & +  0.23 y_{5} & -3.82 y_{17} & -3.23 y_{11}\\
 y_{15}   &  0.0720612400305 & +  0.20 y_{10} & +  0.03 y_{7} & -0.63 y_{14} & -0.85 y_{13} & -0.05 y_{4} & -0.09 y_{1} & +  0.03 y_{5} & -0.34 y_{17} & -0.82 y_{11}\\
 y_{8}   &  0.342992264839 & +  3.15 y_{10} & +  0.32 y_{7} & +  4.65 y_{14} & -17.79 y_{13} & +  0.03 y_{4} & -0.51 y_{1} & +  0.82 y_{5} & -8.46 y_{17} & -0.06 y_{11}\\
 y_{9}   &  1.51152258427 & -3.15 y_{10} & -0.05 y_{7} & -5.74 y_{14} & -2.28 y_{13} & -0.54 y_{4} & -0.05 y_{1} & +  0.13 y_{5} & +  2.25 y_{17} & -8.32 y_{11}\\
\hline
z    &  6.60318223718 & -53.50 y_{10} & -1.01 y_{7} & -3.11 y_{14} & -17.90 y_{13} & -2.05 y_{4} & -0.64 y_{1} & -2.90 y_{5} & -11.20 y_{17} & -5.93 y_{11}\\
\end{array}\]
Primal Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  53.5018235742 & +  0.75 x_{16} & +  0.10 x_{12} & -10.36 x_{3} & +  0.37 x_{18} & -6.92 x_{2} & -12.81 x_{6} & -0.20 x_{15} & -3.15 x_{8} & +  3.15 x_{9}\\
 x_{7}   &  1.01022003126 & -0.03 x_{16} & +  0.04 x_{12} & +  0.41 x_{3} & +  0.06 x_{18} & +  0.76 x_{2} & +  0.00 x_{6} & -0.03 x_{15} & -0.32 x_{8} & +  0.05 x_{9}\\
 x_{14}   &  3.1101358663 & +  0.23 x_{16} & -0.21 x_{12} & -9.17 x_{3} & +  0.48 x_{18} & -5.48 x_{2} & +  9.47 x_{6} & +  0.63 x_{15} & -4.65 x_{8} & +  5.74 x_{9}\\
 x_{13}   &  17.9032102922 & -0.41 x_{16} & -0.57 x_{12} & -0.89 x_{3} & -0.35 x_{18} & +  0.37 x_{2} & -1.57 x_{6} & +  0.85 x_{15} & + 17.79 x_{8} & +  2.28 x_{9}\\
 x_{4}   &  2.05081960643 & +  0.04 x_{16} & +  0.04 x_{12} & +  0.11 x_{3} & +  0.02 x_{18} & -0.00 x_{2} & -0.08 x_{6} & +  0.05 x_{15} & -0.03 x_{8} & +  0.54 x_{9}\\
 x_{1}   &  0.641056470683 & -0.05 x_{16} & -0.07 x_{12} & -0.56 x_{3} & -0.00 x_{18} & +  0.80 x_{2} & +  0.23 x_{6} & +  0.09 x_{15} & +  0.51 x_{8} & +  0.05 x_{9}\\
 x_{5}   &  2.90108612881 & +  0.05 x_{16} & +  0.00 x_{12} & -0.04 x_{3} & +  0.04 x_{18} & -0.26 x_{2} & -0.23 x_{6} & -0.03 x_{15} & -0.82 x_{8} & -0.13 x_{9}\\
 x_{17}   &  11.1976273496 & -0.97 x_{16} & -0.55 x_{12} & +  2.41 x_{3} & -0.58 x_{18} & -2.18 x_{2} & +  3.82 x_{6} & +  0.34 x_{15} & +  8.46 x_{8} & -2.25 x_{9}\\
 x_{11}   &  5.92990260911 & +  0.23 x_{16} & -0.13 x_{12} & -11.02 x_{3} & +  0.91 x_{18} & + 19.16 x_{2} & +  3.23 x_{6} & +  0.82 x_{15} & +  0.06 x_{8} & +  8.32 x_{9}\\
\hline
z    &  -6.60318223718 & -0.01 x_{16} & -0.01 x_{12} & -0.91 x_{3} & -0.12 x_{18} & -2.29 x_{2} & -0.92 x_{6} & -0.07 x_{15} & -0.34 x_{8} & -1.51 x_{9}\\
\end{array}\]
Primal Dictionary with original objective is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  53.5018235742 & +  0.75 x_{16} & +  0.10 x_{12} & -10.36 x_{3} & +  0.37 x_{18} & -6.92 x_{2} & -12.81 x_{6} & -0.20 x_{15} & -3.15 x_{8} & +  3.15 x_{9}\\
 x_{7}   &  1.01022003126 & -0.03 x_{16} & +  0.04 x_{12} & +  0.41 x_{3} & +  0.06 x_{18} & +  0.76 x_{2} & +  0.00 x_{6} & -0.03 x_{15} & -0.32 x_{8} & +  0.05 x_{9}\\
 x_{14}   &  3.1101358663 & +  0.23 x_{16} & -0.21 x_{12} & -9.17 x_{3} & +  0.48 x_{18} & -5.48 x_{2} & +  9.47 x_{6} & +  0.63 x_{15} & -4.65 x_{8} & +  5.74 x_{9}\\
 x_{13}   &  17.9032102922 & -0.41 x_{16} & -0.57 x_{12} & -0.89 x_{3} & -0.35 x_{18} & +  0.37 x_{2} & -1.57 x_{6} & +  0.85 x_{15} & + 17.79 x_{8} & +  2.28 x_{9}\\
 x_{4}   &  2.05081960643 & +  0.04 x_{16} & +  0.04 x_{12} & +  0.11 x_{3} & +  0.02 x_{18} & -0.00 x_{2} & -0.08 x_{6} & +  0.05 x_{15} & -0.03 x_{8} & +  0.54 x_{9}\\
 x_{1}   &  0.641056470683 & -0.05 x_{16} & -0.07 x_{12} & -0.56 x_{3} & -0.00 x_{18} & +  0.80 x_{2} & +  0.23 x_{6} & +  0.09 x_{15} & +  0.51 x_{8} & +  0.05 x_{9}\\
 x_{5}   &  2.90108612881 & +  0.05 x_{16} & +  0.00 x_{12} & -0.04 x_{3} & +  0.04 x_{18} & -0.26 x_{2} & -0.23 x_{6} & -0.03 x_{15} & -0.82 x_{8} & -0.13 x_{9}\\
 x_{17}   &  11.1976273496 & -0.97 x_{16} & -0.55 x_{12} & +  2.41 x_{3} & -0.58 x_{18} & -2.18 x_{2} & +  3.82 x_{6} & +  0.34 x_{15} & +  8.46 x_{8} & -2.25 x_{9}\\
 x_{11}   &  5.92990260911 & +  0.23 x_{16} & -0.13 x_{12} & -11.02 x_{3} & +  0.91 x_{18} & + 19.16 x_{2} & +  3.23 x_{6} & +  0.82 x_{15} & +  0.06 x_{8} & +  8.32 x_{9}\\
\hline
z    &  17.3706865456 & -0.03 x_{16} & -0.11 x_{12} & +  1.10 x_{3} & +  0.20 x_{18} & +  3.48 x_{2} & +  3.50 x_{6} & +  0.60 x_{15} & -0.74 x_{8} & +  0.88 x_{9}\\
\end{array}\]
\section{Optimization Phase Simplex}
Starting Dictionary is:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  53.5018235742 & +  0.75 x_{16} & +  0.10 x_{12} & -10.36 x_{3} & +  0.37 x_{18} & -6.92 x_{2} & -12.81 x_{6} & -0.20 x_{15} & -3.15 x_{8} & +  3.15 x_{9}\\
 x_{7}   &  1.01022003126 & -0.03 x_{16} & +  0.04 x_{12} & +  0.41 x_{3} & +  0.06 x_{18} & +  0.76 x_{2} & +  0.00 x_{6} & -0.03 x_{15} & -0.32 x_{8} & +  0.05 x_{9}\\
 x_{14}   &  3.1101358663 & +  0.23 x_{16} & -0.21 x_{12} & -9.17 x_{3} & +  0.48 x_{18} & -5.48 x_{2} & +  9.47 x_{6} & +  0.63 x_{15} & -4.65 x_{8} & +  5.74 x_{9}\\
 x_{13}   &  17.9032102922 & -0.41 x_{16} & -0.57 x_{12} & -0.89 x_{3} & -0.35 x_{18} & +  0.37 x_{2} & -1.57 x_{6} & +  0.85 x_{15} & + 17.79 x_{8} & +  2.28 x_{9}\\
 x_{4}   &  2.05081960643 & +  0.04 x_{16} & +  0.04 x_{12} & +  0.11 x_{3} & +  0.02 x_{18} & -0.00 x_{2} & -0.08 x_{6} & +  0.05 x_{15} & -0.03 x_{8} & +  0.54 x_{9}\\
 x_{1}   &  0.641056470683 & -0.05 x_{16} & -0.07 x_{12} & -0.56 x_{3} & -0.00 x_{18} & +  0.80 x_{2} & +  0.23 x_{6} & +  0.09 x_{15} & +  0.51 x_{8} & +  0.05 x_{9}\\
 x_{5}   &  2.90108612881 & +  0.05 x_{16} & +  0.00 x_{12} & -0.04 x_{3} & +  0.04 x_{18} & -0.26 x_{2} & -0.23 x_{6} & -0.03 x_{15} & -0.82 x_{8} & -0.13 x_{9}\\
 x_{17}   &  11.1976273496 & -0.97 x_{16} & -0.55 x_{12} & +  2.41 x_{3} & -0.58 x_{18} & -2.18 x_{2} & +  3.82 x_{6} & +  0.34 x_{15} & +  8.46 x_{8} & -2.25 x_{9}\\
 x_{11}   &  5.92990260911 & +  0.23 x_{16} & -0.13 x_{12} & -11.02 x_{3} & +  0.91 x_{18} & + 19.16 x_{2} & +  3.23 x_{6} & +  0.82 x_{15} & +  0.06 x_{8} & +  8.32 x_{9}\\
\hline
z    &  17.3706865456 & -0.03 x_{16} & -0.11 x_{12} & +  1.10 x_{3} & +  0.20 x_{18} & +  3.48 x_{2} & +  3.50 x_{6} & +  0.60 x_{15} & -0.74 x_{8} & +  0.88 x_{9}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  49.5734392603 & +  0.46 x_{16} & +  0.37 x_{12} & +  1.23 x_{3} & -0.23 x_{18} & +  1.26 x_{14} & -24.78 x_{6} & -1.00 x_{15} & +  2.72 x_{8} & -4.10 x_{9}\\
 x_{7}   &  1.43927489795 & -0.00 x_{16} & +  0.01 x_{12} & -0.85 x_{3} & +  0.13 x_{18} & -0.14 x_{14} & +  1.31 x_{6} & +  0.06 x_{15} & -0.96 x_{8} & +  0.84 x_{9}\\
 x_{2}   &  0.567682043629 & +  0.04 x_{16} & -0.04 x_{12} & -1.67 x_{3} & +  0.09 x_{18} & -0.18 x_{14} & +  1.73 x_{6} & +  0.11 x_{15} & -0.85 x_{8} & +  1.05 x_{9}\\
 x_{13}   &  18.1141201773 & -0.39 x_{16} & -0.59 x_{12} & -1.51 x_{3} & -0.32 x_{18} & -0.07 x_{14} & -0.93 x_{6} & +  0.90 x_{15} & + 17.47 x_{8} & +  2.67 x_{9}\\
 x_{4}   &  2.04938623828 & +  0.04 x_{16} & +  0.04 x_{12} & +  0.11 x_{3} & +  0.02 x_{18} & +  0.00 x_{14} & -0.09 x_{6} & +  0.04 x_{15} & -0.03 x_{8} & +  0.54 x_{9}\\
 x_{1}   &  1.09529766346 & -0.01 x_{16} & -0.10 x_{12} & -1.90 x_{3} & +  0.07 x_{18} & -0.15 x_{14} & +  1.61 x_{6} & +  0.18 x_{15} & -0.17 x_{8} & +  0.89 x_{9}\\
 x_{5}   &  2.75344920921 & +  0.04 x_{16} & +  0.01 x_{12} & +  0.39 x_{3} & +  0.02 x_{18} & +  0.05 x_{14} & -0.68 x_{6} & -0.06 x_{15} & -0.60 x_{8} & -0.40 x_{9}\\
 x_{17}   &  9.95953854482 & -1.06 x_{16} & -0.47 x_{12} & +  6.06 x_{3} & -0.77 x_{18} & +  0.40 x_{14} & +  0.05 x_{6} & +  0.09 x_{15} & + 10.32 x_{8} & -4.53 x_{9}\\
 x_{11}   &  16.8051397972 & +  1.02 x_{16} & -0.86 x_{12} & -43.09 x_{3} & +  2.57 x_{18} & -3.50 x_{14} & + 36.35 x_{6} & +  3.01 x_{15} & -16.20 x_{8} & + 28.38 x_{9}\\
\hline
z    &  19.3484615722 & +  0.11 x_{16} & -0.24 x_{12} & -4.73 x_{3} & +  0.50 x_{18} & -0.64 x_{14} & +  9.52 x_{6} & +  0.99 x_{15} & -3.70 x_{8} & +  4.53 x_{9}\\
\end{array}\]


 $ x_{6} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  2.00087220512 & +  0.02 x_{16} & +  0.01 x_{12} & +  0.05 x_{3} & -0.01 x_{18} & +  0.05 x_{14} & -0.04 x_{10} & -0.04 x_{15} & +  0.11 x_{8} & -0.17 x_{9}\\
 x_{7}   &  4.06316371296 & +  0.02 x_{16} & +  0.03 x_{12} & -0.79 x_{3} & +  0.12 x_{18} & -0.07 x_{14} & -0.05 x_{10} & +  0.01 x_{15} & -0.82 x_{8} & +  0.63 x_{9}\\
 x_{2}   &  4.02725094764 & +  0.07 x_{16} & -0.01 x_{12} & -1.59 x_{3} & +  0.07 x_{18} & -0.09 x_{14} & -0.07 x_{10} & +  0.05 x_{15} & -0.66 x_{8} & +  0.76 x_{9}\\
 x_{13}   &  16.2527109517 & -0.41 x_{16} & -0.60 x_{12} & -1.56 x_{3} & -0.31 x_{18} & -0.12 x_{14} & +  0.04 x_{10} & +  0.93 x_{15} & + 17.37 x_{8} & +  2.83 x_{9}\\
 x_{4}   &  1.87425246943 & +  0.03 x_{16} & +  0.04 x_{12} & +  0.11 x_{3} & +  0.02 x_{18} & -0.00 x_{14} & +  0.00 x_{10} & +  0.05 x_{15} & -0.04 x_{8} & +  0.55 x_{9}\\
 x_{1}   &  4.31926663907 & +  0.02 x_{16} & -0.08 x_{12} & -1.82 x_{3} & +  0.05 x_{18} & -0.06 x_{14} & -0.07 x_{10} & +  0.11 x_{15} & +  0.01 x_{8} & +  0.62 x_{9}\\
 x_{5}   &  1.38860606032 & +  0.03 x_{16} & -0.00 x_{12} & +  0.36 x_{3} & +  0.03 x_{18} & +  0.01 x_{14} & +  0.03 x_{10} & -0.03 x_{15} & -0.67 x_{8} & -0.29 x_{9}\\
 x_{17}   &  10.0532310859 & -1.06 x_{16} & -0.47 x_{12} & +  6.07 x_{3} & -0.77 x_{18} & +  0.40 x_{14} & -0.00 x_{10} & +  0.09 x_{15} & + 10.32 x_{8} & -4.54 x_{9}\\
 x_{11}   &  89.5388160805 & +  1.69 x_{16} & -0.33 x_{12} & -41.29 x_{3} & +  2.23 x_{18} & -1.64 x_{14} & -1.47 x_{10} & +  1.55 x_{15} & -12.21 x_{8} & + 22.37 x_{9}\\
\hline
z    &  38.3947309835 & +  0.29 x_{16} & -0.10 x_{12} & -4.26 x_{3} & +  0.41 x_{18} & -0.15 x_{14} & -0.38 x_{10} & +  0.61 x_{15} & -2.65 x_{8} & +  2.95 x_{9}\\
\end{array}\]


 $ x_{9} $ enters and $ x_{17} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  1.63461281397 & +  0.06 x_{16} & +  0.03 x_{12} & -0.17 x_{3} & +  0.02 x_{18} & +  0.04 x_{14} & -0.04 x_{10} & -0.04 x_{15} & -0.27 x_{8} & +  0.04 x_{17}\\
 x_{7}   &  5.44816410535 & -0.12 x_{16} & -0.03 x_{12} & +  0.05 x_{3} & +  0.01 x_{18} & -0.02 x_{14} & -0.05 x_{10} & +  0.02 x_{15} & +  0.61 x_{8} & -0.14 x_{17}\\
 x_{2}   &  5.71291977419 & -0.10 x_{16} & -0.09 x_{12} & -0.57 x_{3} & -0.06 x_{18} & -0.03 x_{14} & -0.07 x_{10} & +  0.06 x_{15} & +  1.07 x_{8} & -0.17 x_{17}\\
 x_{13}   &  22.5114135259 & -1.07 x_{16} & -0.89 x_{12} & +  2.22 x_{3} & -0.78 x_{18} & +  0.13 x_{14} & +  0.04 x_{10} & +  0.99 x_{15} & + 23.79 x_{8} & -0.62 x_{17}\\
 x_{4}   &  3.09461335387 & -0.09 x_{16} & -0.02 x_{12} & +  0.85 x_{3} & -0.07 x_{18} & +  0.04 x_{14} & +  0.00 x_{10} & +  0.06 x_{15} & +  1.21 x_{8} & -0.12 x_{17}\\
 x_{1}   &  5.70192265224 & -0.13 x_{16} & -0.14 x_{12} & -0.99 x_{3} & -0.05 x_{18} & -0.01 x_{14} & -0.07 x_{10} & +  0.12 x_{15} & +  1.43 x_{8} & -0.14 x_{17}\\
 x_{5}   &  0.74420389383 & +  0.10 x_{16} & +  0.03 x_{12} & -0.03 x_{3} & +  0.08 x_{18} & -0.01 x_{14} & +  0.03 x_{10} & -0.04 x_{15} & -1.33 x_{8} & +  0.06 x_{17}\\
 x_{9}   &  2.21477985038 & -0.23 x_{16} & -0.10 x_{12} & +  1.34 x_{3} & -0.17 x_{18} & +  0.09 x_{14} & -0.00 x_{10} & +  0.02 x_{15} & +  2.27 x_{8} & -0.22 x_{17}\\
 x_{11}   &  139.080374572 & -3.52 x_{16} & -2.62 x_{12} & -11.41 x_{3} & -1.55 x_{18} & +  0.33 x_{14} & -1.48 x_{10} & +  1.97 x_{15} & + 38.65 x_{8} & -4.93 x_{17}\\
\hline
z    &  44.9364069967 & -0.40 x_{16} & -0.41 x_{12} & -0.31 x_{3} & -0.09 x_{18} & +  0.11 x_{14} & -0.39 x_{10} & +  0.67 x_{15} & +  4.07 x_{8} & -0.65 x_{17}\\
\end{array}\]


 $ x_{8} $ enters and $ x_{5} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  1.48606974478 & +  0.04 x_{16} & +  0.03 x_{12} & -0.17 x_{3} & +  0.00 x_{18} & +  0.04 x_{14} & -0.05 x_{10} & -0.04 x_{15} & +  0.20 x_{5} & +  0.02 x_{17}\\
 x_{7}   &  5.78607841474 & -0.08 x_{16} & -0.02 x_{12} & +  0.03 x_{3} & +  0.04 x_{18} & -0.02 x_{14} & -0.04 x_{10} & +  0.00 x_{15} & -0.45 x_{5} & -0.11 x_{17}\\
 x_{2}   &  6.31117793259 & -0.03 x_{16} & -0.07 x_{12} & -0.60 x_{3} & +  0.00 x_{18} & -0.04 x_{14} & -0.05 x_{10} & +  0.03 x_{15} & -0.80 x_{5} & -0.12 x_{17}\\
 x_{13}   &  35.7935613611 & +  0.66 x_{16} & -0.36 x_{12} & +  1.68 x_{3} & +  0.58 x_{18} & -0.10 x_{14} & +  0.53 x_{10} & +  0.30 x_{15} & -17.85 x_{5} & +  0.52 x_{17}\\
 x_{4}   &  3.77091414252 & -0.01 x_{16} & +  0.01 x_{12} & +  0.82 x_{3} & -0.00 x_{18} & +  0.03 x_{14} & +  0.03 x_{10} & +  0.02 x_{15} & -0.91 x_{5} & -0.06 x_{17}\\
 x_{1}   &  6.50055461849 & -0.03 x_{16} & -0.11 x_{12} & -1.02 x_{3} & +  0.03 x_{18} & -0.02 x_{14} & -0.04 x_{10} & +  0.08 x_{15} & -1.07 x_{5} & -0.07 x_{17}\\
 x_{8}   &  0.558198007804 & +  0.07 x_{16} & +  0.02 x_{12} & -0.02 x_{3} & +  0.06 x_{18} & -0.01 x_{14} & +  0.02 x_{10} & -0.03 x_{15} & -0.75 x_{5} & +  0.05 x_{17}\\
 x_{9}   &  3.48401076479 & -0.07 x_{16} & -0.05 x_{12} & +  1.28 x_{3} & -0.04 x_{18} & +  0.07 x_{14} & +  0.05 x_{10} & -0.05 x_{15} & -1.71 x_{5} & -0.11 x_{17}\\
 x_{11}   &  160.657256945 & -0.70 x_{16} & -1.76 x_{12} & -12.28 x_{3} & +  0.66 x_{18} & -0.05 x_{14} & -0.67 x_{10} & +  0.85 x_{15} & -28.99 x_{5} & -3.07 x_{17}\\
\hline
z    &  47.2060359764 & -0.10 x_{16} & -0.31 x_{12} & -0.41 x_{3} & +  0.15 x_{18} & +  0.07 x_{14} & -0.30 x_{10} & +  0.55 x_{15} & -3.05 x_{5} & -0.46 x_{17}\\
\end{array}\]


 $ x_{14} $ enters and $ x_{8} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  3.72183926486 & +  0.33 x_{16} & +  0.12 x_{12} & -0.26 x_{3} & +  0.23 x_{18} & -4.01 x_{8} & +  0.04 x_{10} & -0.15 x_{15} & -2.80 x_{5} & +  0.22 x_{17}\\
 x_{7}   &  4.53460402765 & -0.24 x_{16} & -0.07 x_{12} & +  0.08 x_{3} & -0.08 x_{18} & +  2.24 x_{8} & -0.09 x_{10} & +  0.07 x_{15} & +  1.23 x_{5} & -0.22 x_{17}\\
 x_{2}   &  4.15105453926 & -0.31 x_{16} & -0.15 x_{12} & -0.51 x_{3} & -0.22 x_{18} & +  3.87 x_{8} & -0.13 x_{10} & +  0.14 x_{15} & +  2.10 x_{5} & -0.30 x_{17}\\
 x_{13}   &  30.2013475643 & -0.07 x_{16} & -0.58 x_{12} & +  1.91 x_{3} & +  0.00 x_{18} & + 10.02 x_{8} & +  0.32 x_{10} & +  0.59 x_{15} & -10.33 x_{5} & +  0.04 x_{17}\\
 x_{4}   &  5.653353119 & +  0.24 x_{16} & +  0.08 x_{12} & +  0.74 x_{3} & +  0.19 x_{18} & -3.37 x_{8} & +  0.10 x_{10} & -0.07 x_{15} & -3.44 x_{5} & +  0.10 x_{17}\\
 x_{1}   &  5.19547703676 & -0.20 x_{16} & -0.16 x_{12} & -0.97 x_{3} & -0.10 x_{18} & +  2.34 x_{8} & -0.08 x_{10} & +  0.15 x_{15} & +  0.68 x_{5} & -0.18 x_{17}\\
 x_{14}   &  57.3560367171 & +  7.48 x_{16} & +  2.30 x_{12} & -2.32 x_{3} & +  5.88 x_{18} & -102.75 x_{8} & +  2.13 x_{10} & -2.98 x_{15} & -77.07 x_{5} & +  4.94 x_{17}\\
 x_{9}   &  7.27504248738 & +  0.43 x_{16} & +  0.10 x_{12} & +  1.13 x_{3} & +  0.35 x_{18} & -6.79 x_{8} & +  0.19 x_{10} & -0.24 x_{15} & -6.80 x_{5} & +  0.22 x_{17}\\
 x_{11}   &  158.006040978 & -1.05 x_{16} & -1.86 x_{12} & -12.17 x_{3} & +  0.39 x_{18} & +  4.75 x_{8} & -0.77 x_{10} & +  0.99 x_{15} & -25.43 x_{5} & -3.30 x_{17}\\
\hline
z    &  51.243133087 & +  0.42 x_{16} & -0.15 x_{12} & -0.57 x_{3} & +  0.56 x_{18} & -7.23 x_{8} & -0.15 x_{10} & +  0.34 x_{15} & -8.47 x_{5} & -0.11 x_{17}\\
\end{array}\]


 $ x_{15} $ enters and $ x_{14} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{6}   &  0.801109212863 & -0.05 x_{16} & -0.00 x_{12} & -0.14 x_{3} & -0.07 x_{18} & +  1.23 x_{8} & -0.07 x_{10} & +  0.05 x_{14} & +  1.12 x_{5} & -0.04 x_{17}\\
 x_{7}   &  5.7864420188 & -0.08 x_{16} & -0.02 x_{12} & +  0.03 x_{3} & +  0.04 x_{18} & -0.00 x_{8} & -0.04 x_{10} & -0.02 x_{14} & -0.45 x_{5} & -0.11 x_{17}\\
 x_{2}   &  6.85505163142 & +  0.05 x_{16} & -0.04 x_{12} & -0.62 x_{3} & +  0.06 x_{18} & -0.97 x_{8} & -0.03 x_{10} & -0.05 x_{14} & -1.53 x_{5} & -0.07 x_{17}\\
 x_{13}   &  41.5068917634 & +  1.41 x_{16} & -0.13 x_{12} & +  1.45 x_{3} & +  1.16 x_{18} & -10.24 x_{8} & +  0.74 x_{10} & -0.20 x_{14} & -25.52 x_{5} & +  1.01 x_{17}\\
 x_{4}   &  4.22223980206 & +  0.05 x_{16} & +  0.03 x_{12} & +  0.80 x_{3} & +  0.04 x_{18} & -0.81 x_{8} & +  0.05 x_{10} & +  0.02 x_{14} & -1.52 x_{5} & -0.02 x_{17}\\
 x_{1}   &  8.09902291644 & +  0.18 x_{16} & -0.04 x_{12} & -1.09 x_{3} & +  0.19 x_{18} & -2.86 x_{8} & +  0.02 x_{10} & -0.05 x_{14} & -3.22 x_{5} & +  0.07 x_{17}\\
 x_{15}   &  19.2569889668 & +  2.51 x_{16} & +  0.77 x_{12} & -0.78 x_{3} & +  1.98 x_{18} & -34.50 x_{8} & +  0.72 x_{10} & -0.34 x_{14} & -25.88 x_{5} & +  1.66 x_{17}\\
 x_{9}   &  2.57546097978 & -0.19 x_{16} & -0.09 x_{12} & +  1.32 x_{3} & -0.13 x_{18} & +  1.63 x_{8} & +  0.01 x_{10} & +  0.08 x_{14} & -0.48 x_{5} & -0.19 x_{17}\\
 x_{11}   &  176.979394562 & +  1.43 x_{16} & -1.10 x_{12} & -12.94 x_{3} & +  2.34 x_{18} & -29.24 x_{8} & -0.07 x_{10} & -0.33 x_{14} & -50.93 x_{5} & -1.66 x_{17}\\
\hline
z    &  57.7901096589 & +  1.28 x_{16} & +  0.11 x_{12} & -0.83 x_{3} & +  1.23 x_{18} & -18.96 x_{8} & +  0.09 x_{10} & -0.11 x_{14} & -17.27 x_{5} & +  0.46 x_{17}\\
\end{array}\]


 $ x_{10} $ enters and $ x_{6} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  11.2414322492 & -0.73 x_{16} & -0.02 x_{12} & -1.93 x_{3} & -0.94 x_{18} & + 17.22 x_{8} & -14.03 x_{6} & +  0.71 x_{14} & + 15.72 x_{5} & -0.50 x_{17}\\
 x_{7}   &  5.32981411937 & -0.05 x_{16} & -0.02 x_{12} & +  0.11 x_{3} & +  0.08 x_{18} & -0.70 x_{8} & +  0.57 x_{6} & -0.05 x_{14} & -1.09 x_{5} & -0.09 x_{17}\\
 x_{2}   &  6.5440610312 & +  0.07 x_{16} & -0.04 x_{12} & -0.56 x_{3} & +  0.09 x_{18} & -1.45 x_{8} & +  0.39 x_{6} & -0.07 x_{14} & -1.97 x_{5} & -0.06 x_{17}\\
 x_{13}   &  49.8502798838 & +  0.87 x_{16} & -0.15 x_{12} & +  0.01 x_{3} & +  0.47 x_{18} & +  2.54 x_{8} & -10.41 x_{6} & +  0.33 x_{14} & -13.86 x_{5} & +  0.65 x_{17}\\
 x_{4}   &  4.73039042018 & +  0.02 x_{16} & +  0.03 x_{12} & +  0.71 x_{3} & +  0.00 x_{18} & -0.03 x_{8} & -0.63 x_{6} & +  0.06 x_{14} & -0.80 x_{5} & -0.05 x_{17}\\
 x_{1}   &  8.36630529772 & +  0.17 x_{16} & -0.04 x_{12} & -1.13 x_{3} & +  0.17 x_{18} & -2.45 x_{8} & -0.33 x_{6} & -0.03 x_{14} & -2.85 x_{5} & +  0.06 x_{17}\\
 x_{15}   &  27.3007392711 & +  1.99 x_{16} & +  0.76 x_{12} & -2.16 x_{3} & +  1.31 x_{18} & -22.18 x_{8} & -10.04 x_{6} & +  0.18 x_{14} & -14.63 x_{5} & +  1.30 x_{17}\\
 x_{9}   &  2.72143886251 & -0.20 x_{16} & -0.09 x_{12} & +  1.30 x_{3} & -0.14 x_{18} & +  1.85 x_{8} & -0.18 x_{6} & +  0.09 x_{14} & -0.28 x_{5} & -0.20 x_{17}\\
 x_{11}   &  176.212003118 & +  1.48 x_{16} & -1.10 x_{12} & -12.81 x_{3} & +  2.40 x_{18} & -30.42 x_{8} & +  0.96 x_{6} & -0.38 x_{14} & -52.00 x_{5} & -1.63 x_{17}\\
\hline
z    &  58.8263539526 & +  1.21 x_{16} & +  0.11 x_{12} & -1.01 x_{3} & +  1.14 x_{18} & -17.37 x_{8} & -1.29 x_{6} & -0.05 x_{14} & -15.82 x_{5} & +  0.41 x_{17}\\
\end{array}\]


 $ x_{12} $ enters and $ x_{9} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  10.5712379936 & -0.68 x_{16} & +  0.25 x_{9} & -2.25 x_{3} & -0.90 x_{18} & + 16.76 x_{8} & -13.99 x_{6} & +  0.69 x_{14} & + 15.79 x_{5} & -0.45 x_{17}\\
 x_{7}   &  4.79322305229 & -0.01 x_{16} & +  0.20 x_{9} & -0.14 x_{3} & +  0.11 x_{18} & -1.07 x_{8} & +  0.61 x_{6} & -0.07 x_{14} & -1.04 x_{5} & -0.05 x_{17}\\
 x_{2}   &  5.18116328709 & +  0.16 x_{16} & +  0.50 x_{9} & -1.21 x_{3} & +  0.16 x_{18} & -2.38 x_{8} & +  0.48 x_{6} & -0.11 x_{14} & -1.83 x_{5} & +  0.04 x_{17}\\
 x_{13}   &  45.3847385272 & +  1.19 x_{16} & +  1.64 x_{9} & -2.11 x_{3} & +  0.71 x_{18} & -0.49 x_{8} & -10.12 x_{6} & +  0.18 x_{14} & -13.40 x_{5} & +  0.97 x_{17}\\
 x_{4}   &  5.50586979723 & -0.04 x_{16} & -0.28 x_{9} & +  1.08 x_{3} & -0.04 x_{18} & +  0.50 x_{8} & -0.69 x_{6} & +  0.08 x_{14} & -0.88 x_{5} & -0.10 x_{17}\\
 x_{1}   &  6.99759871932 & +  0.26 x_{16} & +  0.50 x_{9} & -1.78 x_{3} & +  0.24 x_{18} & -3.39 x_{8} & -0.24 x_{6} & -0.08 x_{14} & -2.71 x_{5} & +  0.16 x_{17}\\
 x_{15}   &  50.5288153682 & +  0.33 x_{16} & -8.54 x_{9} & +  8.90 x_{3} & +  0.07 x_{18} & -6.38 x_{8} & -11.60 x_{6} & +  0.95 x_{14} & -17.03 x_{5} & -0.37 x_{17}\\
 x_{12}   &  30.742529349 & -2.21 x_{16} & -11.30 x_{9} & + 14.65 x_{3} & -1.63 x_{18} & + 20.91 x_{8} & -2.06 x_{6} & +  1.03 x_{14} & -3.17 x_{5} & -2.21 x_{17}\\
 x_{11}   &  142.306563501 & +  3.91 x_{16} & + 12.46 x_{9} & -28.96 x_{3} & +  4.20 x_{18} & -53.48 x_{8} & +  3.23 x_{6} & -1.52 x_{14} & -48.50 x_{5} & +  0.81 x_{17}\\
\hline
z    &  62.1294023479 & +  0.97 x_{16} & -1.21 x_{9} & +  0.56 x_{3} & +  0.97 x_{18} & -15.13 x_{8} & -1.51 x_{6} & +  0.06 x_{14} & -16.16 x_{5} & +  0.17 x_{17}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{1} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  1.73343305909 & -1.01 x_{16} & -0.39 x_{9} & +  1.26 x_{1} & -1.21 x_{18} & + 21.04 x_{8} & -13.68 x_{6} & +  0.79 x_{14} & + 19.20 x_{5} & -0.64 x_{17}\\
 x_{7}   &  4.22483171279 & -0.03 x_{16} & +  0.16 x_{9} & +  0.08 x_{1} & +  0.09 x_{18} & -0.79 x_{8} & +  0.63 x_{6} & -0.06 x_{14} & -0.82 x_{5} & -0.06 x_{17}\\
 x_{2}   &  0.419446522064 & -0.02 x_{16} & +  0.16 x_{9} & +  0.68 x_{1} & -0.01 x_{18} & -0.07 x_{8} & +  0.64 x_{6} & -0.06 x_{14} & +  0.01 x_{5} & -0.06 x_{17}\\
 x_{13}   &  37.0922961855 & +  0.88 x_{16} & +  1.04 x_{9} & +  1.19 x_{1} & +  0.42 x_{18} & +  3.52 x_{8} & -9.83 x_{6} & +  0.28 x_{14} & -10.19 x_{5} & +  0.78 x_{17}\\
 x_{4}   &  9.75153328347 & +  0.13 x_{16} & +  0.02 x_{9} & -0.61 x_{1} & +  0.11 x_{18} & -1.56 x_{8} & -0.83 x_{6} & +  0.04 x_{14} & -2.53 x_{5} & -0.01 x_{17}\\
 x_{3}   &  3.92326103216 & +  0.15 x_{16} & +  0.28 x_{9} & -0.56 x_{1} & +  0.14 x_{18} & -1.90 x_{8} & -0.14 x_{6} & -0.04 x_{14} & -1.52 x_{5} & +  0.09 x_{17}\\
 x_{15}   &  85.459237098 & +  1.65 x_{16} & -6.02 x_{9} & -4.99 x_{1} & +  1.29 x_{18} & -23.28 x_{8} & -12.80 x_{6} & +  0.56 x_{14} & -30.53 x_{5} & +  0.41 x_{17}\\
 x_{12}   &  88.2002991773 & -0.03 x_{16} & -7.17 x_{9} & -8.21 x_{1} & +  0.37 x_{18} & -6.88 x_{8} & -4.05 x_{6} & +  0.38 x_{14} & -25.39 x_{5} & -0.93 x_{17}\\
 x_{11}   &  28.6963350785 & -0.38 x_{16} & +  4.29 x_{9} & + 16.24 x_{1} & +  0.24 x_{18} & +  1.48 x_{8} & +  7.16 x_{6} & -0.23 x_{14} & -4.57 x_{5} & -1.72 x_{17}\\
\hline
z    &  64.3328347046 & +  1.06 x_{16} & -1.06 x_{9} & -0.31 x_{1} & +  1.05 x_{18} & -16.19 x_{8} & -1.59 x_{6} & +  0.04 x_{14} & -17.02 x_{5} & +  0.22 x_{17}\\
\end{array}\]


 $ x_{14} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  7.4168797954 & -1.24 x_{16} & +  1.76 x_{9} & + 10.48 x_{1} & -1.32 x_{18} & + 20.03 x_{8} & -4.95 x_{6} & -13.55 x_{2} & + 19.37 x_{5} & -1.50 x_{17}\\
 x_{7}   &  3.77749360614 & -0.01 x_{16} & -0.01 x_{9} & -0.64 x_{1} & +  0.10 x_{18} & -0.71 x_{8} & -0.06 x_{6} & +  1.07 x_{2} & -0.83 x_{5} & +  0.01 x_{17}\\
 x_{14}   &  7.17135549872 & -0.29 x_{16} & +  2.71 x_{9} & + 11.63 x_{1} & -0.15 x_{18} & -1.27 x_{8} & + 11.01 x_{6} & -17.10 x_{2} & +  0.21 x_{5} & -1.08 x_{17}\\
 x_{13}   &  39.084398977 & +  0.80 x_{16} & +  1.80 x_{9} & +  4.42 x_{1} & +  0.38 x_{18} & +  3.17 x_{8} & -6.77 x_{6} & -4.75 x_{2} & -10.13 x_{5} & +  0.48 x_{17}\\
 x_{4}   &  10.0025575448 & +  0.12 x_{16} & +  0.12 x_{9} & -0.20 x_{1} & +  0.10 x_{18} & -1.60 x_{8} & -0.45 x_{6} & -0.60 x_{2} & -2.52 x_{5} & -0.05 x_{17}\\
 x_{3}   &  3.60358056266 & +  0.16 x_{16} & +  0.16 x_{9} & -1.08 x_{1} & +  0.14 x_{18} & -1.84 x_{8} & -0.63 x_{6} & +  0.76 x_{2} & -1.53 x_{5} & +  0.14 x_{17}\\
 x_{15}   &  89.4552429668 & +  1.49 x_{16} & -4.51 x_{9} & +  1.49 x_{1} & +  1.21 x_{18} & -23.98 x_{8} & -6.67 x_{6} & -9.53 x_{2} & -30.41 x_{5} & -0.19 x_{17}\\
 x_{12}   &  90.9079283887 & -0.14 x_{16} & -6.14 x_{9} & -3.82 x_{1} & +  0.32 x_{18} & -7.36 x_{8} & +  0.11 x_{6} & -6.46 x_{2} & -25.31 x_{5} & -1.34 x_{17}\\
 x_{11}   &  27.0818414322 & -0.32 x_{16} & +  3.68 x_{9} & + 13.62 x_{1} & +  0.27 x_{18} & +  1.77 x_{8} & +  4.68 x_{6} & +  3.85 x_{2} & -4.61 x_{5} & -1.47 x_{17}\\
\hline
z    &  64.6010230179 & +  1.05 x_{16} & -0.95 x_{9} & +  0.12 x_{1} & +  1.04 x_{18} & -16.24 x_{8} & -1.18 x_{6} & -0.64 x_{2} & -17.01 x_{5} & +  0.18 x_{17}\\
\end{array}\]


 $ x_{1} $ enters and $ x_{3} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  42.4194312796 & +  0.32 x_{16} & +  3.32 x_{9} & -9.71 x_{3} & +  0.07 x_{18} & +  2.15 x_{8} & -11.04 x_{6} & -6.15 x_{2} & +  4.54 x_{5} & -0.19 x_{17}\\
 x_{7}   &  1.62559241706 & -0.11 x_{16} & -0.11 x_{9} & +  0.60 x_{3} & +  0.01 x_{18} & +  0.39 x_{8} & +  0.31 x_{6} & +  0.61 x_{2} & +  0.08 x_{5} & -0.08 x_{17}\\
 x_{14}   &  46.0165876777 & +  1.45 x_{16} & +  4.45 x_{9} & -10.78 x_{3} & +  1.40 x_{18} & -21.12 x_{8} & +  4.26 x_{6} & -8.88 x_{2} & -16.24 x_{5} & +  0.38 x_{17}\\
 x_{13}   &  53.8317535545 & +  1.46 x_{16} & +  2.46 x_{9} & -4.09 x_{3} & +  0.96 x_{18} & -4.37 x_{8} & -9.33 x_{6} & -1.63 x_{2} & -16.38 x_{5} & +  1.04 x_{17}\\
 x_{4}   &  9.336492891 & +  0.09 x_{16} & +  0.09 x_{9} & +  0.18 x_{3} & +  0.08 x_{18} & -1.26 x_{8} & -0.33 x_{6} & -0.74 x_{2} & -2.24 x_{5} & -0.07 x_{17}\\
 x_{1}   &  3.33886255924 & +  0.15 x_{16} & +  0.15 x_{9} & -0.93 x_{3} & +  0.13 x_{18} & -1.71 x_{8} & -0.58 x_{6} & +  0.71 x_{2} & -1.41 x_{5} & +  0.13 x_{17}\\
 x_{15}   &  94.4336492891 & +  1.71 x_{16} & -4.29 x_{9} & -1.38 x_{3} & +  1.41 x_{18} & -26.53 x_{8} & -7.53 x_{6} & -8.47 x_{2} & -32.52 x_{5} & -0.01 x_{17}\\
 x_{12}   &  78.1587677725 & -0.71 x_{16} & -6.71 x_{9} & +  3.54 x_{3} & -0.19 x_{18} & -0.85 x_{8} & +  2.33 x_{6} & -9.15 x_{2} & -19.91 x_{5} & -1.82 x_{17}\\
 x_{11}   &  72.5450236967 & +  1.72 x_{16} & +  5.72 x_{9} & -12.62 x_{3} & +  2.08 x_{18} & -21.46 x_{8} & -3.23 x_{6} & + 13.46 x_{2} & -23.88 x_{5} & +  0.24 x_{17}\\
\hline
z    &  65.0023696682 & +  1.06 x_{16} & -0.94 x_{9} & -0.11 x_{3} & +  1.06 x_{18} & -16.45 x_{8} & -1.25 x_{6} & -0.55 x_{2} & -17.18 x_{5} & +  0.20 x_{17}\\
\end{array}\]


 $ x_{16} $ enters and $ x_{7} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  47.2608695652 & -2.98 x_{7} & +  3.00 x_{9} & -7.93 x_{3} & +  0.11 x_{18} & +  3.30 x_{8} & -10.11 x_{6} & -4.33 x_{2} & +  4.78 x_{5} & -0.41 x_{17}\\
 x_{16}   &  14.9130434783 & -9.17 x_{7} & -1.00 x_{9} & +  5.48 x_{3} & +  0.13 x_{18} & +  3.57 x_{8} & +  2.87 x_{6} & +  5.61 x_{2} & +  0.74 x_{5} & -0.70 x_{17}\\
 x_{14}   &  67.6086956522 & -13.28 x_{7} & +  3.00 x_{9} & -2.85 x_{3} & +  1.59 x_{18} & -15.96 x_{8} & +  8.41 x_{6} & -0.76 x_{2} & -15.17 x_{5} & -0.63 x_{17}\\
 x_{13}   &  75.5652173913 & -13.37 x_{7} & +  1.00 x_{9} & +  3.89 x_{3} & +  1.15 x_{18} & +  0.83 x_{8} & -5.15 x_{6} & +  6.54 x_{2} & -15.30 x_{5} & +  0.02 x_{17}\\
 x_{4}   &  10.6086956522 & -0.78 x_{7} & +  0.00 x_{9} & +  0.65 x_{3} & +  0.09 x_{18} & -0.96 x_{8} & -0.09 x_{6} & -0.26 x_{2} & -2.17 x_{5} & -0.13 x_{17}\\
 x_{1}   &  5.5652173913 & -1.37 x_{7} & -0.00 x_{9} & -0.11 x_{3} & +  0.15 x_{18} & -1.17 x_{8} & -0.15 x_{6} & +  1.54 x_{2} & -1.30 x_{5} & +  0.02 x_{17}\\
 x_{15}   &  119.913043478 & -15.67 x_{7} & -6.00 x_{9} & +  7.98 x_{3} & +  1.63 x_{18} & -20.43 x_{8} & -2.63 x_{6} & +  1.11 x_{2} & -31.26 x_{5} & -1.20 x_{17}\\
 x_{12}   &  67.5217391304 & +  6.54 x_{7} & -6.00 x_{9} & -0.37 x_{3} & -0.28 x_{18} & -3.39 x_{8} & +  0.28 x_{6} & -13.15 x_{2} & -20.43 x_{5} & -1.33 x_{17}\\
 x_{11}   &  98.1304347826 & -15.74 x_{7} & +  4.00 x_{9} & -3.22 x_{3} & +  2.30 x_{18} & -15.35 x_{8} & +  1.70 x_{6} & + 23.09 x_{2} & -22.61 x_{5} & -0.96 x_{17}\\
\hline
z    &  80.8695652174 & -9.76 x_{7} & -2.00 x_{9} & +  5.72 x_{3} & +  1.20 x_{18} & -12.65 x_{8} & +  1.80 x_{6} & +  5.41 x_{2} & -16.39 x_{5} & -0.54 x_{17}\\
\end{array}\]


 $ x_{2} $ enters and $ x_{12} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{10}   &  25.0512396694 & -5.13 x_{7} & +  4.97 x_{9} & -7.81 x_{3} & +  0.20 x_{18} & +  4.42 x_{8} & -10.20 x_{6} & +  0.33 x_{12} & + 11.50 x_{5} & +  0.02 x_{17}\\
 x_{16}   &  43.7074380165 & -6.38 x_{7} & -3.56 x_{9} & +  5.32 x_{3} & +  0.01 x_{18} & +  2.12 x_{8} & +  2.99 x_{6} & -0.43 x_{12} & -7.98 x_{5} & -1.26 x_{17}\\
 x_{14}   &  63.7024793388 & -13.66 x_{7} & +  3.35 x_{9} & -2.83 x_{3} & +  1.60 x_{18} & -15.76 x_{8} & +  8.40 x_{6} & +  0.06 x_{12} & -13.99 x_{5} & -0.55 x_{17}\\
 x_{13}   &  109.158677686 & -10.11 x_{7} & -1.99 x_{9} & +  3.71 x_{3} & +  1.01 x_{18} & -0.86 x_{8} & -5.01 x_{6} & -0.50 x_{12} & -25.47 x_{5} & -0.64 x_{17}\\
 x_{4}   &  9.2694214876 & -0.91 x_{7} & +  0.12 x_{9} & +  0.66 x_{3} & +  0.09 x_{18} & -0.89 x_{8} & -0.09 x_{6} & +  0.02 x_{12} & -1.77 x_{5} & -0.10 x_{17}\\
 x_{1}   &  13.4892561983 & -0.60 x_{7} & -0.70 x_{9} & -0.15 x_{3} & +  0.12 x_{18} & -1.57 x_{8} & -0.12 x_{6} & -0.12 x_{12} & -3.70 x_{5} & -0.13 x_{17}\\
 x_{15}   &  125.604958678 & -15.12 x_{7} & -6.51 x_{9} & +  7.95 x_{3} & +  1.61 x_{18} & -20.72 x_{8} & -2.61 x_{6} & -0.08 x_{12} & -32.98 x_{5} & -1.31 x_{17}\\
 x_{2}   &  5.13388429752 & +  0.50 x_{7} & -0.46 x_{9} & -0.03 x_{3} & -0.02 x_{18} & -0.26 x_{8} & +  0.02 x_{6} & -0.08 x_{12} & -1.55 x_{5} & -0.10 x_{17}\\
 x_{11}   &  216.656198347 & -4.25 x_{7} & -6.53 x_{9} & -3.87 x_{3} & +  1.81 x_{18} & -21.30 x_{8} & +  2.19 x_{6} & -1.76 x_{12} & -58.48 x_{5} & -3.28 x_{17}\\
\hline
z    &  108.659504132 & -7.07 x_{7} & -4.47 x_{9} & +  5.57 x_{3} & +  1.08 x_{18} & -14.05 x_{8} & +  1.92 x_{6} & -0.41 x_{12} & -24.80 x_{5} & -1.09 x_{17}\\
\end{array}\]


 $ x_{3} $ enters and $ x_{10} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  3.20626189972 & -0.66 x_{7} & +  0.64 x_{9} & -0.13 x_{10} & +  0.03 x_{18} & +  0.57 x_{8} & -1.31 x_{6} & +  0.04 x_{12} & +  1.47 x_{5} & +  0.00 x_{17}\\
 x_{16}   &  60.7668711656 & -9.88 x_{7} & -0.17 x_{9} & -0.68 x_{10} & +  0.15 x_{18} & +  5.13 x_{8} & -3.96 x_{6} & -0.20 x_{12} & -0.14 x_{5} & -1.25 x_{17}\\
 x_{14}   &  54.6401523165 & -11.81 x_{7} & +  1.55 x_{9} & +  0.36 x_{10} & +  1.53 x_{18} & -17.36 x_{8} & + 12.09 x_{6} & -0.06 x_{12} & -18.15 x_{5} & -0.56 x_{17}\\
 x_{13}   &  121.045694944 & -12.55 x_{7} & +  0.37 x_{9} & -0.47 x_{10} & +  1.11 x_{18} & +  1.24 x_{8} & -9.85 x_{6} & -0.34 x_{12} & -20.01 x_{5} & -0.63 x_{17}\\
 x_{4}   &  11.3839644595 & -1.35 x_{7} & +  0.54 x_{9} & -0.08 x_{10} & +  0.11 x_{18} & -0.52 x_{8} & -0.95 x_{6} & +  0.05 x_{12} & -0.80 x_{5} & -0.10 x_{17}\\
 x_{1}   &  13.0016924053 & -0.50 x_{7} & -0.80 x_{9} & +  0.02 x_{10} & +  0.12 x_{18} & -1.66 x_{8} & +  0.08 x_{6} & -0.12 x_{12} & -3.93 x_{5} & -0.13 x_{17}\\
 x_{15}   &  151.085466469 & -20.34 x_{7} & -1.45 x_{9} & -1.02 x_{10} & +  1.81 x_{18} & -16.23 x_{8} & -12.98 x_{6} & +  0.25 x_{12} & -21.28 x_{5} & -1.28 x_{17}\\
 x_{2}   &  5.04379098794 & +  0.52 x_{7} & -0.47 x_{9} & +  0.00 x_{10} & -0.02 x_{18} & -0.27 x_{8} & +  0.06 x_{6} & -0.08 x_{12} & -1.60 x_{5} & -0.10 x_{17}\\
 x_{11}   &  204.26041887 & -1.71 x_{7} & -8.99 x_{9} & +  0.49 x_{10} & +  1.71 x_{18} & -23.49 x_{8} & +  7.24 x_{6} & -1.92 x_{12} & -64.17 x_{5} & -3.30 x_{17}\\
\hline
z    &  126.503279035 & -10.72 x_{7} & -0.93 x_{9} & -0.71 x_{10} & +  1.22 x_{18} & -10.90 x_{8} & -5.35 x_{6} & -0.18 x_{12} & -16.61 x_{5} & -1.07 x_{17}\\
\end{array}\]


 $ x_{18} $ enters and $ x_{2} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  9.06666666667 & -0.06 x_{7} & +  0.09 x_{9} & -0.12 x_{10} & -1.16 x_{2} & +  0.25 x_{8} & -1.24 x_{6} & -0.05 x_{12} & -0.38 x_{5} & -0.11 x_{17}\\
 x_{16}   &  94.2 & -6.46 x_{7} & -3.31 x_{9} & -0.66 x_{10} & -6.63 x_{2} & +  3.31 x_{8} & -3.57 x_{6} & -0.71 x_{12} & -10.71 x_{5} & -1.91 x_{17}\\
 x_{14}   &  402.133333333 & + 23.74 x_{7} & -31.11 x_{9} & +  0.61 x_{10} & -68.90 x_{2} & -36.22 x_{8} & + 16.10 x_{6} & -5.38 x_{12} & -128.05 x_{5} & -7.51 x_{17}\\
 x_{13}   &  372.466666667 & + 13.17 x_{7} & -23.26 x_{9} & -0.30 x_{10} & -49.85 x_{2} & -12.41 x_{8} & -6.95 x_{6} & -4.19 x_{12} & -99.52 x_{5} & -5.66 x_{17}\\
 x_{4}   &  36.2666666667 & +  1.20 x_{7} & -1.80 x_{9} & -0.07 x_{10} & -4.93 x_{2} & -1.87 x_{8} & -0.67 x_{6} & -0.33 x_{12} & -8.67 x_{5} & -0.60 x_{17}\\
 x_{1}   &  39.1333333333 & +  2.17 x_{7} & -3.26 x_{9} & +  0.04 x_{10} & -5.18 x_{2} & -3.08 x_{8} & +  0.38 x_{6} & -0.52 x_{12} & -12.19 x_{5} & -0.66 x_{17}\\
 x_{15}   &  562.466666667 & + 21.74 x_{7} & -40.11 x_{9} & -0.72 x_{10} & -81.56 x_{2} & -38.55 x_{8} & -8.24 x_{6} & -6.05 x_{12} & -151.38 x_{5} & -9.51 x_{17}\\
 x_{18}   &  227.066666667 & + 23.23 x_{7} & -21.34 x_{9} & +  0.16 x_{10} & -45.02 x_{2} & -12.32 x_{8} & +  2.62 x_{6} & -3.48 x_{12} & -71.81 x_{5} & -4.54 x_{17}\\
 x_{11}   &  592.2 & + 37.97 x_{7} & -45.46 x_{9} & +  0.77 x_{10} & -76.91 x_{2} & -44.54 x_{8} & + 11.71 x_{6} & -7.86 x_{12} & -186.86 x_{5} & -11.06 x_{17}\\
\hline
z    &  404.2 & + 17.69 x_{7} & -27.03 x_{9} & -0.51 x_{10} & -55.06 x_{2} & -25.97 x_{8} & -2.14 x_{6} & -4.43 x_{12} & -104.43 x_{5} & -6.63 x_{17}\\
\end{array}\]


 $ x_{7} $ enters and $ x_{16} $ leaves 

 \[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{3}   &  8.23303834808 & +  0.01 x_{16} & +  0.12 x_{9} & -0.12 x_{10} & -1.10 x_{2} & +  0.22 x_{8} & -1.21 x_{6} & -0.04 x_{12} & -0.29 x_{5} & -0.10 x_{17}\\
 x_{7}   &  14.5884955752 & -0.15 x_{16} & -0.51 x_{9} & -0.10 x_{10} & -1.03 x_{2} & +  0.51 x_{8} & -0.55 x_{6} & -0.11 x_{12} & -1.66 x_{5} & -0.30 x_{17}\\
 x_{14}   &  748.505899705 & -3.68 x_{16} & -43.30 x_{9} & -1.81 x_{10} & -93.27 x_{2} & -24.03 x_{8} & +  2.96 x_{6} & -8.01 x_{12} & -167.44 x_{5} & -14.55 x_{17}\\
 x_{13}   &  564.6179941 & -2.04 x_{16} & -30.02 x_{9} & -1.64 x_{10} & -63.37 x_{2} & -5.65 x_{8} & -14.24 x_{6} & -5.65 x_{12} & -121.38 x_{5} & -9.56 x_{17}\\
 x_{4}   &  53.7728613569 & -0.19 x_{16} & -2.42 x_{9} & -0.19 x_{10} & -6.17 x_{2} & -1.25 x_{8} & -1.33 x_{6} & -0.47 x_{12} & -10.66 x_{5} & -0.96 x_{17}\\
 x_{1}   &  70.8112094395 & -0.34 x_{16} & -4.37 x_{9} & -0.18 x_{10} & -7.41 x_{2} & -1.96 x_{8} & -0.82 x_{6} & -0.76 x_{12} & -15.79 x_{5} & -1.30 x_{17}\\
 x_{15}   &  879.662241888 & -3.37 x_{16} & -51.27 x_{9} & -2.94 x_{10} & -103.88 x_{2} & -27.39 x_{8} & -20.26 x_{6} & -8.45 x_{12} & -187.46 x_{5} & -15.96 x_{17}\\
 x_{18}   &  565.936578171 & -3.60 x_{16} & -33.27 x_{9} & -2.20 x_{10} & -68.86 x_{2} & -0.40 x_{8} & -10.23 x_{6} & -6.05 x_{12} & -110.35 x_{5} & -11.43 x_{17}\\
 x_{11}   &  1146.1460177 & -5.88 x_{16} & -64.95 x_{9} & -3.09 x_{10} & -115.89 x_{2} & -25.05 x_{8} & -9.29 x_{6} & -12.06 x_{12} & -249.86 x_{5} & -22.31 x_{17}\\
\hline
z    &  662.207964602 & -2.74 x_{16} & -36.11 x_{9} & -2.31 x_{10} & -73.21 x_{2} & -16.89 x_{8} & -11.92 x_{6} & -6.38 x_{12} & -133.77 x_{5} & -11.87 x_{17}\\
\end{array}\]
Final Dictionary
Solution:  662.207964602
Num Pivots:  17
\end{document}
